SOLUTION: A collection of nickels dimes and quarters amount to $10.00 there are 140 coins and there is twice as many dimes as quarters, find the number of nickels

Your equations are

 n +   d +   q =  140,    (1)
5n + 10d + 25q = 1000,    (2)
d = 2q.                   (3)

(three equations in 3 unknowns). Substitute (3) into (1) and (2). 
In this way you eliminate d and reduce the system to 2 equations in 2 unknowns:

n + 2q + q = 140,         (4)   (instead of (1))
5n + 10*2q + 25q = 1000.  (5)   (instead of (2))

Now simplify equations (4) and (5)

 n +  3q =  140,          (6)
5n + 45q = 1000.          (7)

Next express n = 140 - 3q from (6) and substitute it into (7). You will get a single equation for q

5*(140-3q) + 45q = 1000.  (8)

Simplify (8)

700 - 15q + 45q = 1000,
30q = 1000-700 = 300,

q =  = 10.

Now n = 140 - 3q = 140 - 3*10 = 140 - 30 = 110,  and
    d = 2q = 2*10 = 20.

Answer. n = 110,  d = 20  and  q = 10.